Continuum Mechanics Using Mathematica® Fundamentals, Applications, and Scientific Computing |
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Author:
| Romano, Antonio Lancellotta, Renato Marasco, Addolorata |
Series title: | Modeling and Simulation in Science, Engineering and Technology Ser. |
ISBN: | 978-0-8176-3240-3 |
Publication Date: | Jan 2005 |
Publisher: | Birkhäuser Boston
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Book Format: | Mixed media product |
List Price: | AUD $152.95 |
Book Description:
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The motion of any body depends both on its characteristics and the forces acting on it. Although taking into account all possible properties makes the equations too complex to solve, sometimes it is possible to consider only the properties that have the greatest in?uence on the motion. Models of ideals bodies, which contain only the most relevant properties, can be studied using the tools of mathematical physics. Adding more properties into a model makes it more realistic, but it also...
More DescriptionThe motion of any body depends both on its characteristics and the forces acting on it. Although taking into account all possible properties makes the equations too complex to solve, sometimes it is possible to consider only the properties that have the greatest in?uence on the motion. Models of ideals bodies, which contain only the most relevant properties, can be studied using the tools of mathematical physics. Adding more properties into a model makes it more realistic, but it also makes the motion problem harder to solve. In order to highlight the above statements, let us ?rst suppose that a systemS ofN unconstrainedbodiesC ,i=1,. . . ,N,issu?cientlydescribed i by the model of N material points whenever the bodies have negligible dimensions with respect to the dimensions of the region containing the trajectories. ThismeansthatallthephysicalpropertiesofC thatin?uence i the motion are expressed by a positive number, themass m , whereas the i position of C with respect to a frame I is given by the position vector i r (t) versus time. To determine the functionsr (t), one has to integrate the i i following system of Newtonian equations: m¨ r =F ?f (r ,. . . ,r ,r ? ,. . . ,r ? ,t), i i i i 1 N 1 N i=1,. . .